If $A = < 2, 6, - 3 >$ $A= <2 ,6 ,-3 >$ and $B = < - 6, 4, 0 >$ $B= <-6 ,4 ,0 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2018-02-26T14:58:19

$12 - 14 \sqrt{13}$ $12-14sqrt13$ .

$A = < 2, 6, - 3 > and B = < - 6, 4, 0 >$ $A=<2,6,-3> and B=<-6,4,0>$ .

$:. A*B=(2)(-6)+(6)(4)+(-3)(0)=-12+24+0$ ,

$rArr A*B=12$ .

Further, $||A||=sqrt{(2)^2+(6)^2+(-3)^2}=sqrt(4+36+9)=7$ .

$||B||=sqrt(36+16)=2sqrt13$ .

$rArr ||A||*||B||=14sqrt13$ .

Therefore, $A*B-||A||*||B||=12-14sqrt13$ .

If A= <2 ,6 ,-3 >A=<2,6,−3>A= <2 ,6 ,-3 > and B= <-6 ,4 ,0 >B=<−6,4,0>B= <-6 ,4 ,0 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?